$\begingroup$In KSP, you can spin your crew capsules at better than 100 degrees per second using their built-in reaction wheels. I think OP wants to know what more typical torques/rotation rates are achieved, and some discussion of saturation would be helpful also. (In vanilla, KSP reaction wheels don't saturate.)$\endgroup$
– Russell BorogoveAug 13 '15 at 23:06

$\begingroup$This animation shows how MASCOT aboard Hayabusa 2, now in flight so it seems real, will use a reaction wheel to jump around on an asteroid. I suppose it is just a matter of weight ratio and rotation speed.$\endgroup$
– LocalFluffAug 18 '15 at 3:46

2 Answers
2

Background and Physics

Note that there are actually two different but related types of actuators that use conservation of angular momentum1 to control a spacecraft's attitude (both of which may be lumped into "reaction wheel" by KSP):

Reaction wheels (RWs, a.k.a momentum wheels) spin along a fixed axis at a variable speed. They change angular momentum by speeding up or slowing down.

Control moment gyroscopes (CMGs) spin along a rotating axis at a constant speed. They change angular momentum by rotating their spin axis.2

This paper (pdf)3 talks about the two different technologies, and in particular how they "scale." Assuming that two satellites have the same average density, the torque needed required for a given motion scales like $\tau\propto r^5$. Applying this torque to an object rotating with speed $\omega$ requires a power $P=\tau\omega$.

When a reaction wheel applies a torque, it does so by changing the speed of the quickly-spinning wheel (typical speeds are thousands of RPM). However, a CMG rotates the axis of the wheel, so the torque is applied perpendicular to the rotation of the spinning wheel (which moves at a constant speed), so the amount of power used is very small.

Thus from a power consumption standpoint, CMGs win over reaction wheels when very high torques are required. However, even for relatively large satellites reaction wheels are used for their simplicity (which means low size, low mass, and better reliability).

Reaction Wheels in KSP

Let's consider the Mk1 Command Pod from KSP. Using the values from the wiki, we can estimate the moment of inertia as:

$$
I \approx \frac{mr^2}{10} \approx 130~\text{kg}\cdot\text{m}^2
$$

According to the same source, the "reaction wheel" torque is $5~\text{kN}\cdot\text{m}$, enough to apply an angular acceleration on the order of:

The "reaction wheels" seem to be hugely over-spec'd (this is probably because they are typically used to control the attitude of an entire rocket instead of engine gimbaling). Indeed, the torque is far beyond the limits of any CMG flying today: for comparison, the CMGs on the ISS (pdf) have a maximum output torque of just $258~\text{N}\cdot\text{m}$ each. Thus you are correct that reaction wheels in KSP have greatly exaggerated performance.

However, the question remains: are they useless in real life?

Attitude Controller Selection

Although this answer covers the topic quite well, I think it's appropriate to have a discussion here with more of an eye towards reaction wheels and CMGs vs. other solutions.

RW/CMG: Pros

Doesn't use propellant. Spacecraft that are designed to operate for decades, such as communications and weather satellites, are usually limited by the amount of consumables that they carry on board, particularly fuel. (This is especially the case for geostationary satellites, where adding mass is very expensive.) Reaction wheels only use electricity, and solar power can be used indefinitely.

A secondary reason that this quality is nice is that there are no propellant residues to accumulate on and degrade the spacecraft's optics (if it has any).

High accuracy. Reaction wheels are controlled by electric motors, and we can make tiny adjustments to their speed with high accuracy. This enables space telescopes to point within fractions of an arcsecond of their targets.

On the other hand, it is very difficult to scale down thrusters past a certain size. Similarly, thruster burns cannot be arbitrarily short due to mechanical limitations. Therefore there is a minimum correction that can be applied by thrusters, and drift below this level cannot be corrected. Therefore the tighter the pointing requirement, the more frequently thruster firings would be required to keep the spacecraft within the allowable range of error.

RW/CMG: Cons

Mechanically limited lifetime. Typically on a spacecraft anything with a moving part is the first to fail. Reaction wheels in particular, due to their high rotation speed, fail relatively often as this answer covers. For example, Kepler's primary mission was ended when two out of four of its reaction wheels failed, although it continues in a new mission mode. Hubble has also suffered two reaction wheel failures, but the failed units were replaced during Servicing Missions 2 and 3B (however, the failures you hear about in the news are actually the rate-sensing gyros, another mechanical device.)

Added complexity. Unfortunately reaction wheels typically cannot take the place of thrusters. They are still needed to perform maneuvers, particularly orbital corrections or station-keeping over the lifetime of the spacecraft. In addition, reaction wheels cannot counter a net external torque: the reaction wheels will end up slowly gaining angular momentum until they approach their maximum speed. At that point a thruster firing will be required to unload, or "dump" the angular momentum overboard (there do exist other methods to manage excess angular momentum, which I'll talk about later, but all add additional systems and complexity to the spacecraft design and operations). The process of countering the slow buildup of angular momentum from disturbance torques is called momentum management.

(Note that this is in contrast to how reaction wheels work in KSP! In the game, reaction wheels don't saturate; they can apply torque indefinitely.)

Low speed. On large spacecraft, thrusters can be placed far from the axis of rotation to apply larger torques, but reaction wheels apply fixed torque regardless of location. This means that large spacecraft controlled by reaction wheels will turn slowly. For example, Hubble is limited to a slew rate of six angular degrees per minute of time (pdf, p. 18), due to the fact that its reaction wheels have a maximum torque of $0.82~\text{N}\cdot\text{M}$ each (pdf), four orders of magnitude less than the reaction wheels in KSP!

Examples of Momentum Management Strategies

With the above in mind, let's go over a few cases and why reaction wheels are or are not used, in conjunction with other methods:

Manned spacecraft: e.g. the Shuttle or Soyuz, or Apollo. These spacecraft perform lots of maneuvers on-orbit, so they already have a large amount of fuel and powerful thrusters. They also have short mission duration (measured in days; not counting the time they spend docked and inactive) so they don't need a lot of fuel for attitude control. They also don't have high pointing accuracy requirements since they don't have body-mounted science instruments. These factors mean that reaction wheels don't provide any mass savings, and are not used on manned missions.

Space stations: e.g. the ISS or Mir (but I'll mostly be talking about ISS here). The amount of fuel required to stabilize such a massive structure through thrusters alone would be tremendous, so the ISS uses four huge CMGs for stabilization.

The station does have attitude thrusters to perform momentum dumps and large maneuvers, but it can avoid using them (pdf) by balancing the gravity-gradient torque and torque from atmospheric drag against any disturbance torques.

Space telescopes: e.g. Kepler and Hubble. Due to the long mission duration and (usually) no possibility of refueling, in combination with high pointing accuracy requirements, these spacecraft all use reaction wheels. Note that spacecraft in low Earth orbit can use gravity-gradient torque and drag torque (like the ISS), but can also torque against the Earth's magnetic field with magnetorquers to avoid using propellant.

Kepler (in a heliocentric orbit) and JWST (at L2) are too far from the Earth to use these strategies. Both JWST (pdf) and Kepler accumulate angular momentum from photon pressure from the Sun, but in its K2 mission mode (with only two reaction wheels), Kepler carefully balances this photon pressure to zero the disturbance torque and stabilize itself in its third axis.

(Note that attitude control using magnetorquers or photon pressure is especially useful in spacecraft like cubesats or solar sails that may be too small or light for thrusters and or even reaction wheels. )

Deep-space probes: e.g. New Horizons. This answer covers in some detail the attitude control system on New Horizons, but the important takeaway is that it does not use reaction wheels! This is because although the mission duration is very long (9 years to Pluto), most of that time is spent in a spin-stabilized state where no active control is required. Additionally, the very short encounter with the Pluto system means that the spacecraft must be able to make many fast manuvers in a short period. A reaction wheel system capable of this would be far too heavy for New Horizons. Finally, there are reliability issues over such a long mission, and it would be expensive (both in design and testing) to ensure that the reaction wheels would be functional at Pluto, whereas the reliability of the thrusters is required anyway for trajectory correction maneuvers.

So overall, although reaction wheels are not used like they are in KSP, they do have real-world applications.

1 There are two equivalent ways to think about it. One is that reaction wheels and CMGs apply torque to the spacecraft when they change speed or rotate, respectively, and that torque causes the spacecraft to turn.

The other way is that the total angular momentum vector of the spacecraft including the actuators must remain the same (both in direction and magnitude).

When a reaction wheel changes speed, it changes the length of its angular momentum vector, so the angular momentum of the spacecraft (excluding the RW) must change along that axis by an opposite amount, causing the spacecraft to turn.

When a CMG turns its rotation axis, it changes the direction of its angular momentum vector, so the angular momentum of the spacecraft (excluding the CMG) must cancel the change in momentum, causing the spacecraft to turn.

2 I realize that the wording here is a bit confusing, because there are two rotations involved. One is the rotation of a disk spinning about an axle, the other is the rotation of the axle relative to the spacecraft. This demo of precession (youtube) shows visually the two rotations involved.

However, note that the result of the demo would be different in space, since the chair applies torques to the demonstrator to keep him upright: if he were floating in space, he would rotate about the horizontal axes as well as the vertical axis, while the orientation of the wheel would remain more or less unchanged.

They are neither science fiction, nor are they relatively useless. But the areas where they might be used instead of alternatives are fairly limited.

Because they consume power but not mass, they might be preferred for long-duration missions. Apollo and STS were of limited length. Thrusters are more powerful, lighter, and of reduced complexity. For a short-duration mission with limited mass budget, thrusters are a win.

Besides reaction wheels, you can go for a full control moment gyroscope. CMGs will deliver more torque for the same power, but are also more complex. If your vehicle is large, reaction wheels just don't cut it. They're simply impractical above a certain size. You'll want to use CMGs. But for smaller vehicles, the simplicity of a reaction wheel could make it preferable over a CMG.

This paper has some discussion of uses of reaction wheels and control moment gyros and has some figures about each.

$\begingroup$Could you please include most relevant figures from the document you link also in your answer, please? Linked content often becomes unavailable and we also prefer all the information relevant to answering the question here, if and when that is possible. Thanks!$\endgroup$
– TildalWaveAug 13 '15 at 15:19